The strong competition in manufacturing industry has led to a constant search for efficient cutting operations to reduce cost. Increased productivity requires faster machining and lower cycle times. In order to meet these demands it is desired that process parameters, such as cutting speed, feed velocity and depth of cut are taken to the next level. As a consequence of modified process parameters, an increase in cutting forces and temperature in the cutting zone follows. Elevated process temperatures and cutting forces accelerates tool wear and may contribute to work piece distortion. Increased cutting forces also make the machining process more prone to regenerative vibrations. This phenomenon is known as chatter.
Chatter vibrations compromise the quality of the machined work piece surface, it may break the cutting tool, and in extreme cases it may lead to damage of the machine tool. Chatter vibrations can occur in all metal cutting processes and is one of the most common productivity limiting factors in metal machining. One reason for chatter is dynamic force feed-back due to variation in chip thickness during cut. The variation in chip thickness may originate from a phase shift in vibration marks left on the machined surface between two consecutive cuts. This phase shift may thus be dependent on the dynamics of the machine tool/cutting tool assembly. The spindle speed n and number of cutting teeth z govern the period time between cuts. Since the spindle speed is a process parameter to be selected by the operator, this parameter can be chosen so that the vibration marks from the previous cut is in phase with the current cut. If the vibration marks between cuts is in phase then force feed-back is at least considerably reduced and as a consequence, also the regenerative vibrations.
To be able to predict the dynamic behaviour of a cutting tool, a stability lobe chart may be plotted. One example of such a chart is shown in FIG. 6. The chart should be read as follows. If a spindle speed (rotational speed, n) in combination with a depth of cut (d) lies below the line, then the cutting process should be stable. If the cutting parameter combination, on the other hand, lies above the line then the process may be unstable.
Regardless of methodology chosen to predict the stability boundary for a cutting process it is advantageous to know the frequency response functions (FRF) at the tool tip of the cutting tool mounted in the machine tool. The state-of-the-art is to obtain the FRFs at the tool tip by physical testing of a multitude of machine-tool/cutting tool combinations. The downside to this approach is that not only is it required to obtain the FRFs for all cutting tools of interest, since the dynamic properties changes with the variation in geometric properties for the different cutting tools, but it also requires that the machine tool is still standing during measurements. This results in loss of valuable production time.
On the other hand, modelling of a complete machine tool structure, i.e. the combined system of a machine tool with mounted cutting tool, would be hard because of the mechanical complexity of the complete system. Thus it is a problem to simplify predictions on the dynamic behaviour of a complete machine tool system.